Question

A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid.

Answer 1

We have,

Radius of cone = radius of hemisphere =r = 3.5 cm or AD = BD = CI

Total height of the solid, OC = 9.5 cm 

`rArr OD + CD = 9.5`

`rArr OD + 3.5 = 9.5` 

`rArr OD = 6  cm`

⇒ Height of cone, h = 6 cm

Now,

Volume of solid = Volume of cone + Volume of hemisphere

`= 1/3pir^2h + 2/3pir^3`

`=1/3 pir^2 (h + 2r)`

`=1/3xx22/7xx3.5xx3.5xx(6+2xx3.5)`

`= 1/3xx 22/7xx3.5xx3.5xx(6+7)`

`= 1/3xx22/7xx3.5xx3.5xx13`

`= 500.5/3`

≈ 166.83 cm³ 

So, the volume of the solid is 166.83 cm^3.